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# Population Mean Corresponding

6. For a population with a mean of µ =100 and standard deviation of Ï? =10,

a. X =105 X=120 X = 130
X = 90 X = 85 X =60

b. Find the score (X value) that corresponds to each of the following z-scores.
z = 1.00 z = -0.50 z = 2.00
z = 0.70 z = 1.50 z = -1.50

24. Which of the following exams scores should lead the better grade?

a. A score of X = 55 on exam with µ= 60 and Ï? =5

b. A score of X = 40 on exam with µ = 50 and Ï? = 20.

26. A distribution with of µ =38 and a standard deviation of Ï?=20 is being transformed into a standardized distribution with µ=50 and Ï? =10. Find the new, standardized score for each of the following values from the original population.

a. X = 48 b. X = 40
c. X =30 d. X = 18

2. A jar contain 20 red marbles, of which 10 are large and 10 are small, and 30 blue marbles, of which 10 are large and 20 are small. If 1 marble is randomly selected from the jar,
a. What is the probability of obtaining a blue marble?
b. What is the probability of obtaining a large marble?
c. What is the probability of obtaining a large blue marble?

4. What is sampling with replacement, and why is it used?

10. For a normal distribution, identify the z-scores location that that would separate the distribution into two sections so that there is

a. 70% in the right-hand size side.
b.80% in the right-hand size side.
c. 75% in the left-hand size side.
d. 90% % in the left-hand size side.

12. For a normal distribution, find the z-scores values that separate
a. The middle 60% of from the distribution from the 40% in tails.
b. The middle 70% of distribution from the 30% in the tails.
c. The middle 80 % of distribution from the 20% in the tails.
d. The middle 90% of distribution from the 10% in the tails.

18. A normal distribution has a mean of µ = 80 and a standard deviation of Ï? =10. For each of the following scores, indicate whether the body of the distribution is to the left or right of the scores, and find the proportion of the distribution in the body.
a. X = 85 b. X =92
c. X= 78 c. X = 72

#### Solution Preview

6. a ) Given mean  = 100 and standard deviation = 10 . The Z scores are given by .
i.
ii.
iii.
iv.
v.
vi.

b)
i.
ii.
iii.
iv.
v.
vi.

24. The Z score corresponding to (a) is
The Z score corresponding to (b) is
Clearly (b) lead to a better grade because is greater than . This means the number of students who secured lesser marks in case (a) is greater than that of case ...

#### Solution Summary

The population mean corresponding are examined.

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